Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4900,2,Mod(1,4900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4900.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4900 = 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4900.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(39.1266969904\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.28825\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4900.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.28825 | −1.32112 | −0.660560 | − | 0.750774i | \(-0.729681\pi\) | ||||
−0.660560 | + | 0.750774i | \(0.729681\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.23607 | 0.745356 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.47214 | −1.64991 | −0.824956 | − | 0.565198i | \(-0.808800\pi\) | ||||
−0.824956 | + | 0.565198i | \(0.808800\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.874032 | 0.242413 | 0.121206 | − | 0.992627i | \(-0.461324\pi\) | ||||
0.121206 | + | 0.992627i | \(0.461324\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.57649 | −1.10996 | −0.554981 | − | 0.831863i | \(-0.687275\pi\) | ||||
−0.554981 | + | 0.831863i | \(0.687275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.99070 | −1.37436 | −0.687181 | − | 0.726486i | \(-0.741152\pi\) | ||||
−0.687181 | + | 0.726486i | \(0.741152\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.47214 | −0.723990 | −0.361995 | − | 0.932180i | \(-0.617904\pi\) | ||||
−0.361995 | + | 0.932180i | \(0.617904\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.74806 | 0.336415 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.236068 | 0.0438367 | 0.0219184 | − | 0.999760i | \(-0.493023\pi\) | ||||
0.0219184 | + | 0.999760i | \(0.493023\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.27895 | −1.48694 | −0.743472 | − | 0.668767i | \(-0.766822\pi\) | ||||
−0.743472 | + | 0.668767i | \(0.766822\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.5216 | 2.17973 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.23607 | 0.696405 | 0.348203 | − | 0.937419i | \(-0.386792\pi\) | ||||
0.348203 | + | 0.937419i | \(0.386792\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.11667 | −0.799090 | −0.399545 | − | 0.916714i | \(-0.630832\pi\) | ||||
−0.399545 | + | 0.916714i | \(0.630832\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.76393 | 0.573994 | 0.286997 | − | 0.957931i | \(-0.407343\pi\) | ||||
0.286997 | + | 0.957931i | \(0.407343\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.91034 | −0.716247 | −0.358123 | − | 0.933674i | \(-0.616583\pi\) | ||||
−0.358123 | + | 0.933674i | \(0.616583\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.4721 | 1.46639 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.7082 | 1.60825 | 0.804123 | − | 0.594463i | \(-0.202635\pi\) | ||||
0.804123 | + | 0.594463i | \(0.202635\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13.7082 | 1.81570 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.95440 | 0.254441 | 0.127220 | − | 0.991874i | \(-0.459394\pi\) | ||||
0.127220 | + | 0.991874i | \(0.459394\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.53244 | −0.964430 | −0.482215 | − | 0.876053i | \(-0.660168\pi\) | ||||
−0.482215 | + | 0.876053i | \(0.660168\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.9443 | −1.70356 | −0.851782 | − | 0.523896i | \(-0.824478\pi\) | ||||
−0.851782 | + | 0.523896i | \(0.824478\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.94510 | 0.956478 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.7082 | 1.98290 | 0.991449 | − | 0.130491i | \(-0.0416554\pi\) | ||||
0.991449 | + | 0.130491i | \(0.0416554\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.53244 | 0.881605 | 0.440803 | − | 0.897604i | \(-0.354694\pi\) | ||||
0.440803 | + | 0.897604i | \(0.354694\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.4721 | −1.29072 | −0.645358 | − | 0.763880i | \(-0.723292\pi\) | ||||
−0.645358 | + | 0.763880i | \(0.723292\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.7082 | −1.18980 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.1877 | −1.33778 | −0.668889 | − | 0.743362i | \(-0.733230\pi\) | ||||
−0.668889 | + | 0.743362i | \(0.733230\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.540182 | −0.0579135 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.86319 | −0.621496 | −0.310748 | − | 0.950492i | \(-0.600580\pi\) | ||||
−0.310748 | + | 0.950492i | \(0.600580\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 18.9443 | 1.96443 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.3516 | −1.66025 | −0.830125 | − | 0.557577i | \(-0.811731\pi\) | ||||
−0.830125 | + | 0.557577i | \(0.811731\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.2361 | −1.22977 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.36861 | −0.335189 | −0.167595 | − | 0.985856i | \(-0.553600\pi\) | ||||
−0.167595 | + | 0.985856i | \(0.553600\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.3848 | 1.81151 | 0.905753 | − | 0.423806i | \(-0.139306\pi\) | ||||
0.905753 | + | 0.423806i | \(0.139306\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.4721 | 1.20573 | 0.602863 | − | 0.797844i | \(-0.294026\pi\) | ||||
0.602863 | + | 0.797844i | \(0.294026\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.4164 | −1.57241 | −0.786203 | − | 0.617968i | \(-0.787956\pi\) | ||||
−0.786203 | + | 0.617968i | \(0.787956\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.69316 | −0.920034 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.7639 | 1.29480 | 0.647401 | − | 0.762150i | \(-0.275856\pi\) | ||||
0.647401 | + | 0.762150i | \(0.275856\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.95440 | 0.180684 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.9443 | 1.72221 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.7082 | 1.05569 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.1803 | −0.992095 | −0.496047 | − | 0.868295i | \(-0.665216\pi\) | ||||
−0.496047 | + | 0.868295i | \(0.665216\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.61280 | −0.758315 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.16073 | 0.188784 | 0.0943918 | − | 0.995535i | \(-0.469909\pi\) | ||||
0.0943918 | + | 0.995535i | \(0.469909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.0000 | 0.854358 | 0.427179 | − | 0.904167i | \(-0.359507\pi\) | ||||
0.427179 | + | 0.904167i | \(0.359507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.3609 | −0.878797 | −0.439399 | − | 0.898292i | \(-0.644808\pi\) | ||||
−0.439399 | + | 0.898292i | \(0.644808\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.2361 | 0.946248 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.78282 | −0.399960 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.70820 | 0.549557 | 0.274779 | − | 0.961507i | \(-0.411395\pi\) | ||||
0.274779 | + | 0.961507i | \(0.411395\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.23607 | 0.670242 | 0.335121 | − | 0.942175i | \(-0.391223\pi\) | ||||
0.335121 | + | 0.942175i | \(0.391223\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.2333 | −0.827317 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.02546 | −0.720310 | −0.360155 | − | 0.932892i | \(-0.617276\pi\) | ||||
−0.360155 | + | 0.932892i | \(0.617276\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −26.7912 | −2.12468 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.18034 | −0.170777 | −0.0853887 | − | 0.996348i | \(-0.527213\pi\) | ||||
−0.0853887 | + | 0.996348i | \(0.527213\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.11512 | −0.318438 | −0.159219 | − | 0.987243i | \(-0.550898\pi\) | ||||
−0.159219 | + | 0.987243i | \(0.550898\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2361 | −0.941236 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.3956 | −1.02439 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.3848 | 1.39777 | 0.698884 | − | 0.715235i | \(-0.253680\pi\) | ||||
0.698884 | + | 0.715235i | \(0.253680\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.47214 | −0.336146 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.70820 | 0.127677 | 0.0638386 | − | 0.997960i | \(-0.479666\pi\) | ||||
0.0638386 | + | 0.997960i | \(0.479666\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.62365 | 0.269344 | 0.134672 | − | 0.990890i | \(-0.457002\pi\) | ||||
0.134672 | + | 0.990890i | \(0.457002\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 17.2361 | 1.27413 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 25.0432 | 1.83134 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.1803 | −0.881338 | −0.440669 | − | 0.897670i | \(-0.645259\pi\) | ||||
−0.440669 | + | 0.897670i | \(0.645259\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.6525 | −1.12669 | −0.563345 | − | 0.826222i | \(-0.690486\pi\) | ||||
−0.563345 | + | 0.826222i | \(0.690486\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.4721 | 1.38733 | 0.693666 | − | 0.720297i | \(-0.255994\pi\) | ||||
0.693666 | + | 0.720297i | \(0.255994\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.6746 | 1.53647 | 0.768235 | − | 0.640168i | \(-0.221135\pi\) | ||||
0.768235 | + | 0.640168i | \(0.221135\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 31.9079 | 2.25061 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.76393 | −0.539631 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 32.7820 | 2.26757 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.52786 | 0.655925 | 0.327963 | − | 0.944691i | \(-0.393638\pi\) | ||||
0.327963 | + | 0.944691i | \(0.393638\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −38.2325 | −2.61965 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −17.2361 | −1.16471 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.8539 | −0.793795 | −0.396898 | − | 0.917863i | \(-0.629913\pi\) | ||||
−0.396898 | + | 0.917863i | \(0.629913\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.40337 | 0.425006 | 0.212503 | − | 0.977160i | \(-0.431838\pi\) | ||||
0.212503 | + | 0.977160i | \(0.431838\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.57804 | 0.368607 | 0.184304 | − | 0.982869i | \(-0.440997\pi\) | ||||
0.184304 | + | 0.982869i | \(0.440997\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.5279 | 0.689703 | 0.344852 | − | 0.938657i | \(-0.387929\pi\) | ||||
0.344852 | + | 0.938657i | \(0.387929\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 26.2511 | 1.70519 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.65248 | 0.559682 | 0.279841 | − | 0.960046i | \(-0.409718\pi\) | ||||
0.279841 | + | 0.960046i | \(0.409718\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.41421 | 0.0910975 | 0.0455488 | − | 0.998962i | \(-0.485496\pi\) | ||||
0.0455488 | + | 0.998962i | \(0.485496\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.2588 | 1.23545 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.23607 | −0.333163 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 27.8885 | 1.76736 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.74806 | −0.110337 | −0.0551684 | − | 0.998477i | \(-0.517570\pi\) | ||||
−0.0551684 | + | 0.998477i | \(0.517570\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.0000 | 1.19452 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.27895 | −0.516427 | −0.258213 | − | 0.966088i | \(-0.583134\pi\) | ||||
−0.258213 | + | 0.966088i | \(0.583134\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.527864 | 0.0326740 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.7082 | −0.660296 | −0.330148 | − | 0.943929i | \(-0.607099\pi\) | ||||
−0.330148 | + | 0.943929i | \(0.607099\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.4164 | 0.821071 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 32.2418 | 1.96582 | 0.982908 | − | 0.184099i | \(-0.0589367\pi\) | ||||
0.982908 | + | 0.184099i | \(0.0589367\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.8369 | 1.50873 | 0.754366 | − | 0.656454i | \(-0.227945\pi\) | ||||
0.754366 | + | 0.656454i | \(0.227945\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.9443 | 1.25842 | 0.629210 | − | 0.777236i | \(-0.283379\pi\) | ||||
0.629210 | + | 0.777236i | \(0.283379\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −18.5123 | −1.10830 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.1246 | −1.43915 | −0.719577 | − | 0.694413i | \(-0.755664\pi\) | ||||
−0.719577 | + | 0.694413i | \(0.755664\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.5672 | −0.628155 | −0.314077 | − | 0.949397i | \(-0.601695\pi\) | ||||
−0.314077 | + | 0.949397i | \(0.601695\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.94427 | 0.232016 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 37.4164 | 2.19339 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.8477 | 1.15951 | 0.579757 | − | 0.814789i | \(-0.303147\pi\) | ||||
0.579757 | + | 0.814789i | \(0.303147\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.56564 | −0.555055 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.03476 | −0.175505 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.70820 | 0.442825 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.7186 | −1.06833 | −0.534164 | − | 0.845381i | \(-0.679374\pi\) | ||||
−0.534164 | + | 0.845381i | \(0.679374\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −42.0689 | −2.39322 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.40802 | 0.533480 | 0.266740 | − | 0.963769i | \(-0.414054\pi\) | ||||
0.266740 | + | 0.963769i | \(0.414054\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.57494 | 0.202068 | 0.101034 | − | 0.994883i | \(-0.467785\pi\) | ||||
0.101034 | + | 0.994883i | \(0.467785\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.416408 | −0.0233878 | −0.0116939 | − | 0.999932i | \(-0.503722\pi\) | ||||
−0.0116939 | + | 0.999932i | \(0.503722\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.29180 | −0.0723267 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −28.5393 | −1.59291 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 27.4164 | 1.52549 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 37.5648 | 2.07734 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.3607 | −0.954229 | −0.477115 | − | 0.878841i | \(-0.658317\pi\) | ||||
−0.477115 | + | 0.878841i | \(0.658317\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.47214 | 0.519070 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.1246 | −0.932837 | −0.466419 | − | 0.884564i | \(-0.654456\pi\) | ||||
−0.466419 | + | 0.884564i | \(0.654456\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −31.4953 | −1.71059 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 45.3035 | 2.45332 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25.3607 | 1.36143 | 0.680716 | − | 0.732547i | \(-0.261669\pi\) | ||||
0.680716 | + | 0.732547i | \(0.261669\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.9427 | 1.87044 | 0.935219 | − | 0.354069i | \(-0.115202\pi\) | ||||
0.935219 | + | 0.354069i | \(0.115202\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.52786 | 0.0815513 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.7751 | 0.626724 | 0.313362 | − | 0.949634i | \(-0.398545\pi\) | ||||
0.313362 | + | 0.949634i | \(0.398545\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.0689 | −1.53420 | −0.767099 | − | 0.641529i | \(-0.778300\pi\) | ||||
−0.767099 | + | 0.641529i | \(0.778300\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.8885 | 0.888871 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −43.3491 | −2.27524 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.78437 | 0.301942 | 0.150971 | − | 0.988538i | \(-0.451760\pi\) | ||||
0.150971 | + | 0.988538i | \(0.451760\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.4412 | −0.595607 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.1246 | 1.55979 | 0.779897 | − | 0.625908i | \(-0.215272\pi\) | ||||
0.779897 | + | 0.625908i | \(0.215272\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.206331 | 0.0106266 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.1246 | 0.520066 | 0.260033 | − | 0.965600i | \(-0.416266\pi\) | ||||
0.260033 | + | 0.965600i | \(0.416266\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 25.5834 | 1.31068 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.5958 | −1.10349 | −0.551746 | − | 0.834012i | \(-0.686038\pi\) | ||||
−0.551746 | + | 0.834012i | \(0.686038\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.41641 | 0.427830 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.18034 | −0.161250 | −0.0806248 | − | 0.996745i | \(-0.525692\pi\) | ||||
−0.0806248 | + | 0.996745i | \(0.525692\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.8902 | 0.803602 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.94427 | −0.249406 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.73877 | −0.388398 | −0.194199 | − | 0.980962i | \(-0.562211\pi\) | ||||
−0.194199 | + | 0.980962i | \(0.562211\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.708204 | 0.0353660 | 0.0176830 | − | 0.999844i | \(-0.494371\pi\) | ||||
0.0176830 | + | 0.999844i | \(0.494371\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.23607 | −0.360454 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.1803 | −1.14901 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.89949 | −0.489499 | −0.244749 | − | 0.969586i | \(-0.578706\pi\) | ||||
−0.244749 | + | 0.969586i | \(0.578706\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.8825 | −1.12871 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 23.7082 | 1.16100 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.4211 | −1.09534 | −0.547671 | − | 0.836694i | \(-0.684485\pi\) | ||||
−0.547671 | + | 0.836694i | \(0.684485\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.5967 | 1.49119 | 0.745597 | − | 0.666397i | \(-0.232164\pi\) | ||||
0.745597 | + | 0.666397i | \(0.232164\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.9799 | −0.533859 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.9443 | 0.528394 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.6525 | 0.705785 | 0.352892 | − | 0.935664i | \(-0.385198\pi\) | ||||
0.352892 | + | 0.935664i | \(0.385198\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.41577 | −0.116094 | −0.0580471 | − | 0.998314i | \(-0.518487\pi\) | ||||
−0.0580471 | + | 0.998314i | \(0.518487\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.8005 | 0.995025 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.7565 | 1.13384 | 0.566918 | − | 0.823774i | \(-0.308136\pi\) | ||||
0.566918 | + | 0.823774i | \(0.308136\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 39.1246 | 1.85887 | 0.929433 | − | 0.368990i | \(-0.120296\pi\) | ||||
0.929433 | + | 0.368990i | \(0.120296\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.3500 | −0.726031 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.76393 | 0.460788 | 0.230394 | − | 0.973097i | \(-0.425998\pi\) | ||||
0.230394 | + | 0.973097i | \(0.425998\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.9991 | 1.31843 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.8461 | −0.885469 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.6525 | −1.19997 | −0.599986 | − | 0.800010i | \(-0.704827\pi\) | ||||
−0.599986 | + | 0.800010i | \(0.704827\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.00000 | −0.373408 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.0193 | 0.792666 | 0.396333 | − | 0.918107i | \(-0.370282\pi\) | ||||
0.396333 | + | 0.918107i | \(0.370282\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.4164 | 0.623513 | 0.311757 | − | 0.950162i | \(-0.399083\pi\) | ||||
0.311757 | + | 0.950162i | \(0.399083\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.5595 | 0.812555 | 0.406277 | − | 0.913750i | \(-0.366827\pi\) | ||||
0.406277 | + | 0.913750i | \(0.366827\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.6525 | 0.951616 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −20.5967 | −0.947039 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 26.1803 | 1.19872 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.4102 | 1.25241 | 0.626203 | − | 0.779660i | \(-0.284608\pi\) | ||||
0.626203 | + | 0.779660i | \(0.284608\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.70246 | 0.168818 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.4721 | −1.42614 | −0.713069 | − | 0.701094i | \(-0.752696\pi\) | ||||
−0.713069 | + | 0.701094i | \(0.752696\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.98915 | 0.225617 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.76393 | 0.0796051 | 0.0398026 | − | 0.999208i | \(-0.487327\pi\) | ||||
0.0398026 | + | 0.999208i | \(0.487327\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.08036 | −0.0486571 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.9443 | −1.20619 | −0.603096 | − | 0.797669i | \(-0.706066\pi\) | ||||
−0.603096 | + | 0.797669i | \(0.706066\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.41641 | 0.420694 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.3153 | −0.549110 | −0.274555 | − | 0.961571i | \(-0.588531\pi\) | ||||
−0.274555 | + | 0.961571i | \(0.588531\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 27.9991 | 1.24348 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.0162 | −0.665580 | −0.332790 | − | 0.943001i | \(-0.607990\pi\) | ||||
−0.332790 | + | 0.943001i | \(0.607990\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.4721 | −0.462356 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.8701 | 1.18174 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −42.0689 | −1.84662 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.5300 | −1.51279 | −0.756394 | − | 0.654117i | \(-0.773041\pi\) | ||||
−0.756394 | + | 0.654117i | \(0.773041\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.90879 | −0.170919 | −0.0854597 | − | 0.996342i | \(-0.527236\pi\) | ||||
−0.0854597 | + | 0.996342i | \(0.527236\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 37.8885 | 1.65045 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.9443 | −0.475838 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.37016 | 0.189649 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.47214 | −0.193710 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.90879 | −0.168677 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.7082 | −0.460382 | −0.230191 | − | 0.973146i | \(-0.573935\pi\) | ||||
−0.230191 | + | 0.973146i | \(0.573935\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.29180 | −0.355835 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.29180 | −0.140747 | −0.0703735 | − | 0.997521i | \(-0.522419\pi\) | ||||
−0.0703735 | + | 0.997521i | \(0.522419\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.8430 | −0.718844 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.41421 | −0.0602475 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.3475 | 0.607924 | 0.303962 | − | 0.952684i | \(-0.401690\pi\) | ||||
0.303962 | + | 0.952684i | \(0.401690\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.28980 | 0.139144 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −57.3050 | −2.41942 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 41.6799 | 1.75660 | 0.878299 | − | 0.478112i | \(-0.158679\pi\) | ||||
0.878299 | + | 0.478112i | \(0.158679\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.9443 | 1.00380 | 0.501898 | − | 0.864927i | \(-0.332635\pi\) | ||||
0.501898 | + | 0.864927i | \(0.332635\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.34752 | 0.181938 | 0.0909691 | − | 0.995854i | \(-0.471004\pi\) | ||||
0.0909691 | + | 0.995854i | \(0.471004\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.8716 | 1.16435 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.5192 | −1.64520 | −0.822602 | − | 0.568617i | \(-0.807479\pi\) | ||||
−0.822602 | + | 0.568617i | \(0.807479\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 35.8167 | 1.48849 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −64.0689 | −2.65346 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.8971 | −1.52291 | −0.761453 | − | 0.648221i | \(-0.775513\pi\) | ||||
−0.761453 | + | 0.648221i | \(0.775513\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 49.5967 | 2.04360 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −44.5570 | −1.83283 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.5424 | 1.25423 | 0.627113 | − | 0.778928i | \(-0.284236\pi\) | ||||
0.627113 | + | 0.778928i | \(0.284236\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −49.5967 | −2.02986 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.52786 | 0.348439 | 0.174220 | − | 0.984707i | \(-0.444260\pi\) | ||||
0.174220 | + | 0.984707i | \(0.444260\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.4481 | −1.32359 | −0.661793 | − | 0.749687i | \(-0.730204\pi\) | ||||
−0.661793 | + | 0.749687i | \(0.730204\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −31.1803 | −1.26976 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.03786 | −0.204480 | −0.102240 | − | 0.994760i | \(-0.532601\pi\) | ||||
−0.102240 | + | 0.994760i | \(0.532601\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.29180 | −0.173627 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.8885 | 1.08602 | 0.543009 | − | 0.839727i | \(-0.317285\pi\) | ||||
0.543009 | + | 0.839727i | \(0.317285\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.3607 | −0.618398 | −0.309199 | − | 0.950997i | \(-0.600061\pi\) | ||||
−0.309199 | + | 0.950997i | \(0.600061\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.1723 | 1.05195 | 0.525976 | − | 0.850500i | \(-0.323700\pi\) | ||||
0.525976 | + | 0.850500i | \(0.323700\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.06952 | −0.243561 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −75.0132 | −2.99574 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19.3863 | −0.772984 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.00000 | −0.0398094 | −0.0199047 | − | 0.999802i | \(-0.506336\pi\) | ||||
−0.0199047 | + | 0.999802i | \(0.506336\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −21.8021 | −0.866555 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 37.3607 | 1.47797 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −39.3607 | −1.55465 | −0.777327 | − | 0.629097i | \(-0.783425\pi\) | ||||
−0.777327 | + | 0.629097i | \(0.783425\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.3786 | 1.04027 | 0.520135 | − | 0.854084i | \(-0.325882\pi\) | ||||
0.520135 | + | 0.854084i | \(0.325882\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.4729 | 0.490360 | 0.245180 | − | 0.969478i | \(-0.421153\pi\) | ||||
0.245180 | + | 0.969478i | \(0.421153\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.6947 | −0.419804 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −35.3050 | −1.38159 | −0.690795 | − | 0.723051i | \(-0.742739\pi\) | ||||
−0.690795 | + | 0.723051i | \(0.742739\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.8430 | 0.657110 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.4721 | 0.641663 | 0.320832 | − | 0.947136i | \(-0.396038\pi\) | ||||
0.320832 | + | 0.947136i | \(0.396038\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.0957 | 1.71512 | 0.857561 | − | 0.514382i | \(-0.171979\pi\) | ||||
0.857561 | + | 0.514382i | \(0.171979\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.15298 | 0.355472 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.819660 | −0.0317374 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 27.1246 | 1.04870 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 41.2185 | 1.59122 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.29180 | −0.319625 | −0.159813 | − | 0.987147i | \(-0.551089\pi\) | ||||
−0.159813 | + | 0.987147i | \(0.551089\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.7788 | −1.18293 | −0.591464 | − | 0.806332i | \(-0.701450\pi\) | ||||
−0.591464 | + | 0.806332i | \(0.701450\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.6525 | −0.561484 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.47214 | 0.362441 | 0.181221 | − | 0.983442i | \(-0.441995\pi\) | ||||
0.181221 | + | 0.983442i | \(0.441995\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.7639 | −0.486974 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.2333 | 0.389859 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.0764 | −1.03003 | −0.515017 | − | 0.857180i | \(-0.672214\pi\) | ||||
−0.515017 | + | 0.857180i | \(0.672214\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.4164 | 0.886960 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24.0903 | −0.911180 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.2492 | 1.29358 | 0.646788 | − | 0.762670i | \(-0.276112\pi\) | ||||
0.646788 | + | 0.762670i | \(0.276112\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.3770 | −0.957113 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.8885 | −0.596707 | −0.298353 | − | 0.954455i | \(-0.596437\pi\) | ||||
−0.298353 | + | 0.954455i | \(0.596437\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −25.6525 | −0.962043 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 28.7456 | 1.07653 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −19.7990 | −0.739407 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.6777 | −0.883028 | −0.441514 | − | 0.897254i | \(-0.645559\pi\) | ||||
−0.441514 | + | 0.897254i | \(0.645559\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.23607 | −0.120351 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.9473 | 1.40739 | 0.703694 | − | 0.710503i | \(-0.251532\pi\) | ||||
0.703694 | + | 0.710503i | \(0.251532\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.9443 | −0.442380 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.2256 | −0.637112 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.1313 | −0.706630 | −0.353315 | − | 0.935504i | \(-0.614946\pi\) | ||||
−0.353315 | + | 0.935504i | \(0.614946\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 76.3050 | 2.81073 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.0557 | −0.664191 | −0.332095 | − | 0.943246i | \(-0.607756\pi\) | ||||
−0.332095 | + | 0.943246i | \(0.607756\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.9814 | 0.440148 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −46.1803 | −1.69419 | −0.847096 | − | 0.531440i | \(-0.821651\pi\) | ||||
−0.847096 | + | 0.531440i | \(0.821651\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −27.2526 | −0.997121 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.94427 | 0.180419 | 0.0902095 | − | 0.995923i | \(-0.471246\pi\) | ||||
0.0902095 | + | 0.995923i | \(0.471246\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.00000 | 0.145768 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 49.7214 | 1.80715 | 0.903577 | − | 0.428426i | \(-0.140932\pi\) | ||||
0.903577 | + | 0.428426i | \(0.140932\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −43.4767 | −1.57810 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −49.9287 | −1.80992 | −0.904958 | − | 0.425501i | \(-0.860098\pi\) | ||||
−0.904958 | + | 0.425501i | \(0.860098\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.70820 | 0.0616797 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.6854 | 0.601692 | 0.300846 | − | 0.953673i | \(-0.402731\pi\) | ||||
0.300846 | + | 0.953673i | \(0.402731\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.9443 | 0.682261 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.94355 | 0.249742 | 0.124871 | − | 0.992173i | \(-0.460148\pi\) | ||||
0.124871 | + | 0.992173i | \(0.460148\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30.6525 | 1.09824 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −91.4296 | −3.27161 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.412662 | 0.0147473 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.4875 | −1.37193 | −0.685966 | − | 0.727634i | \(-0.740620\pi\) | ||||
−0.685966 | + | 0.727634i | \(0.740620\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 24.5030 | 0.872330 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.58359 | −0.233790 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.3972 | −0.509974 | −0.254987 | − | 0.966944i | \(-0.582071\pi\) | ||||
−0.254987 | + | 0.966944i | \(0.582071\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.4721 | 0.795007 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.1105 | −0.463236 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −41.2185 | −1.45457 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −73.7771 | −2.59708 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.8754 | 0.417516 | 0.208758 | − | 0.977967i | \(-0.433058\pi\) | ||||
0.208758 | + | 0.977967i | \(0.433058\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.1545 | −0.356574 | −0.178287 | − | 0.983979i | \(-0.557056\pi\) | ||||
−0.178287 | + | 0.983979i | \(0.557056\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −56.8328 | −1.99321 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.5486 | −0.788876 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.5279 | −0.681527 | −0.340764 | − | 0.940149i | \(-0.610686\pi\) | ||||
−0.340764 | + | 0.940149i | \(0.610686\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.0557 | −0.559667 | −0.279834 | − | 0.960048i | \(-0.590279\pi\) | ||||
−0.279834 | + | 0.960048i | \(0.590279\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.6525 | −1.65704 | −0.828519 | − | 0.559960i | \(-0.810816\pi\) | ||||
−0.828519 | + | 0.559960i | \(0.810816\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43.3491 | −1.50558 | −0.752789 | − | 0.658262i | \(-0.771292\pi\) | ||||
−0.752789 | + | 0.658262i | \(0.771292\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −47.9256 | −1.66252 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −14.4721 | −0.500230 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.5803 | −0.814081 | −0.407040 | − | 0.913410i | \(-0.633439\pi\) | ||||
−0.407040 | + | 0.913410i | \(0.633439\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9443 | −0.998078 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 55.2030 | 1.90129 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24.1803 | 0.829867 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.7082 | −0.504191 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.255039 | −0.00873237 | −0.00436619 | − | 0.999990i | \(-0.501390\pi\) | ||||
−0.00436619 | + | 0.999990i | \(0.501390\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.03941 | −0.206302 | −0.103151 | − | 0.994666i | \(-0.532893\pi\) | ||||
−0.103151 | + | 0.994666i | \(0.532893\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.4096 | −0.355170 | −0.177585 | − | 0.984105i | \(-0.556828\pi\) | ||||
−0.177585 | + | 0.984105i | \(0.556828\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.87539 | −0.336162 | −0.168081 | − | 0.985773i | \(-0.553757\pi\) | ||||
−0.168081 | + | 0.985773i | \(0.553757\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.02546 | −0.306521 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 62.7771 | 2.12957 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.1877 | −0.412966 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −36.5632 | −1.23748 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.4296 | 1.50028 | 0.750140 | − | 0.661279i | \(-0.229986\pi\) | ||||
0.750140 | + | 0.661279i | \(0.229986\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −45.4164 | −1.53186 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.7456 | −0.968465 | −0.484233 | − | 0.874939i | \(-0.660901\pi\) | ||||
−0.484233 | + | 0.874939i | \(0.660901\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.05573 | −0.203791 | −0.101896 | − | 0.994795i | \(-0.532491\pi\) | ||||
−0.101896 | + | 0.994795i | \(0.532491\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −48.4658 | −1.62732 | −0.813661 | − | 0.581339i | \(-0.802529\pi\) | ||||
−0.813661 | + | 0.581339i | \(0.802529\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 58.5967 | 1.96306 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 29.4164 | 0.984383 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.94427 | 0.231862 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.95440 | −0.0651827 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −53.5825 | −1.78509 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.7771 | 0.922323 | 0.461162 | − | 0.887316i | \(-0.347433\pi\) | ||||
0.461162 | + | 0.887316i | \(0.347433\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.53244 | −0.249835 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.11146 | −0.235613 | −0.117807 | − | 0.993037i | \(-0.537586\pi\) | ||||
−0.117807 | + | 0.993037i | \(0.537586\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 66.6930 | 2.20722 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.7082 | 0.617127 | 0.308563 | − | 0.951204i | \(-0.400152\pi\) | ||||
0.308563 | + | 0.951204i | \(0.400152\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 42.8328 | 1.41139 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.6035 | 0.480680 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 41.1096 | 1.35022 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.9991 | 0.918622 | 0.459311 | − | 0.888276i | \(-0.348096\pi\) | ||||
0.459311 | + | 0.888276i | \(0.348096\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21.5279 | −0.704791 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 55.6157 | 1.81689 | 0.908443 | − | 0.418009i | \(-0.137272\pi\) | ||||
0.908443 | + | 0.418009i | \(0.137272\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.18034 | −0.266955 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.78593 | 0.221215 | 0.110607 | − | 0.993864i | \(-0.464720\pi\) | ||||
0.110607 | + | 0.993864i | \(0.464720\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.7658 | 0.578534 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.7771 | −0.512686 | −0.256343 | − | 0.966586i | \(-0.582518\pi\) | ||||
−0.256343 | + | 0.966586i | \(0.582518\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.58359 | 0.213712 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.952843 | 0.0308981 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 55.9017 | 1.81083 | 0.905417 | − | 0.424524i | \(-0.139558\pi\) | ||||
0.905417 | + | 0.424524i | \(0.139558\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.95595 | 0.0955522 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.5410 | 1.21100 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 27.8885 | 0.898696 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.58359 | −0.147398 | −0.0736992 | − | 0.997281i | \(-0.523480\pi\) | ||||
−0.0736992 | + | 0.997281i | \(0.523480\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −62.7355 | −2.01535 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.4729 | −0.400274 | −0.200137 | − | 0.979768i | \(-0.564139\pi\) | ||||
−0.200137 | + | 0.979768i | \(0.564139\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.59675 | −0.211049 | −0.105524 | − | 0.994417i | \(-0.533652\pi\) | ||||
−0.105524 | + | 0.994417i | \(0.533652\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.0841 | 1.02541 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −36.7082 | −1.17200 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42.4751 | 1.35475 | 0.677373 | − | 0.735640i | \(-0.263118\pi\) | ||||
0.677373 | + | 0.735640i | \(0.263118\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.0689 | −0.415566 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.34752 | 0.138104 | 0.0690518 | − | 0.997613i | \(-0.478003\pi\) | ||||
0.0690518 | + | 0.997613i | \(0.478003\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 39.7255 | 1.26065 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.23179 | −0.292374 | −0.146187 | − | 0.989257i | \(-0.546700\pi\) | ||||
−0.146187 | + | 0.989257i | \(0.546700\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.40492 | 0.234281 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4900.2.a.bi.1.1 | yes | 4 | |
5.2 | odd | 4 | 4900.2.e.u.2549.8 | 8 | |||
5.3 | odd | 4 | 4900.2.e.u.2549.2 | 8 | |||
5.4 | even | 2 | 4900.2.a.bg.1.4 | yes | 4 | ||
7.6 | odd | 2 | inner | 4900.2.a.bi.1.4 | yes | 4 | |
35.13 | even | 4 | 4900.2.e.u.2549.7 | 8 | |||
35.27 | even | 4 | 4900.2.e.u.2549.1 | 8 | |||
35.34 | odd | 2 | 4900.2.a.bg.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4900.2.a.bg.1.1 | ✓ | 4 | 35.34 | odd | 2 | ||
4900.2.a.bg.1.4 | yes | 4 | 5.4 | even | 2 | ||
4900.2.a.bi.1.1 | yes | 4 | 1.1 | even | 1 | trivial | |
4900.2.a.bi.1.4 | yes | 4 | 7.6 | odd | 2 | inner | |
4900.2.e.u.2549.1 | 8 | 35.27 | even | 4 | |||
4900.2.e.u.2549.2 | 8 | 5.3 | odd | 4 | |||
4900.2.e.u.2549.7 | 8 | 35.13 | even | 4 | |||
4900.2.e.u.2549.8 | 8 | 5.2 | odd | 4 |